Previously disclosed, in U.S. Pat. Nos. 6,570,361 and 6,351,095, have been High Phase Order electrical rotating machine designs. Of specific interest is the application “HIGH PHASE ORDER MOTOR WITH MESH CONNECTED WINDINGS,” Ser. No. 09/713,654, filed Nov. 15, 2000, now U.S. Pat. No. 6,657,334, which discloses the use of a high phase order concentrated winding machine, connected to an inverter using a mesh connection. When using a mesh connection, the voltage across each winding is a function related to the voltages of both of the two inverter legs that drive that winding, and therefore, may be different from the actual voltages produced by the inverter legs. That machine is deliberately operated either with a fundamental drive waveform, a pure harmonic drive waveform, or admixtures of these, in order to change the volts/hertz ratio of an induction machine, in order to increase the power delivered to the machine by a power electronics drive system when the motor was being operated at low speed and thus reduced slot voltage. In other words, the motor can be operated at higher current than the currents produced in the inverter.
In my previously disclosed machines, extensive use was made of concentrated windings. Concentrated windings place inductors of a single phase in a single slot in each pole of a stator. Motor windings are usually produced using coils of wire, with the portion of a coil residing in one slot forming the inductors for that slot, and the portion of the same coil on the opposite side of the coil is placed in another slot, forming a set of inductors with reverse polarity from the first. These two slots are placed 180 electrical degrees apart, forming so-called full span concentrated windings.
Concentrated windings offer numerous benefits, including the ability to use harmonic components of drive currents to produce useable rotating fields, reduction in chording and distribution factors, which reduce resistance losses, and the ability to use specific harmonic drive waveforms to obtain desired changes in machine impedance. However the use of concentrated windings comes at a significant cost. Each phase in a concentrated winding machine requires separate input terminals, separate inverter output stages, separate wiring and fault detection circuitry, separate logic level PWM, and possibly separate current and voltage measurement. Additionally, if the phase count is not sufficient, then a concentrated winding electrical machine does not make sufficient use of its stator. The stator slots would be few and widely spaced. Concentrated winding induction machines are thus only useful when the phase count can be large.
The standard of industry for electrical rotating machines is the three-phase system. Three phase systems cannot in general use concentrated windings, with the exception of extremely high pole count systems, in which the pole/phase group (PPG) might be limited to a single slot. Rather, three phase systems use distributed and chorded windings in order to make better use of the stator, and to eliminate the deleterious results caused by non-synchronized components in the drive waveform, winding flux distribution, or other sources of spatial harmonic magnetic fields.
In a stator with distributed windings, the series connected inductors of a single phase are placed in a number of slots rather than in single slot or slot pair. Inductors in the various slots somewhat counter the magnetic field produced by the series connected inductors in other slots, reducing the effective current flowing in the inductors, and thus reducing the efficiency of producing a magnetic field. However this reduction in magnetic field strength disproportionately effects harmonic magnetic fields, the net result being that harmonic rotating fields are reduced, reducing low speed torque pulsation and torque cusp, as well as making better use of stator cross section given the low number of phases.
FIG. 1a (prior art) uses arrows to show the flux distribution in a stator incorporating distributed windings, and FIG. 1b uses arrows to show the magnetic field strength in a stator incorporating concentrated windings. A concentrated winding generates a field distribution that is squared. Physically, the field H (theta) is evenly distributed as shown in FIG. 1b. In a distributed winding, the turns of the winding are distributed so that the resultant field distribution is sinusoidal in theta, as depicted in FIG. 1a. 
FIG. 1c shows the graph of a r=Hθ+baseline offset, the sinusoid which the distribution of the windings approximates as much as possible. The ideal approach is to distribute the turns according to the formula dN/dθ=(N/2)sin θ. That is, the turn density in number of turns per radian must be approximately (N/2)sin θ. The highest turn density will be at ±π/2. The result of the sinusoidal distribution is to cancel, to a very large degree, all spatial harmonics.
Spatial and Temporal Harmonics
Spatial harmonics are regular distortions in the magnetic field produced in the stator of a rotating machine. Spatial harmonics with a pole count greater than the pole count of the fundamental are filtered out and do not cause losses, if the windings of the stator are wound with a winding distribution according to the sinusoid function.
Temporal harmonics, which originate with the drive waveform, are currents within the drive waveform that cycle faster than the drive waveform. In a three phase machine, the magnetic fields that these harmonics produce, if they were to be viewed in isolation, would have the same number of poles as the fundamental, eg two poles in a two pole machine. This is because a three-phase machine does not fully sample the high frequencies of the temporal harmonics of the drive waveform. These temporal harmonics therefore would produce a magnetic field in a three phase stator, which seems to be similar in shape to the fundamental and yet rotates faster than the fundamental around the stator, and often in the reverse direction, depending on the specific harmonic involved. This magnetic field would not be filtered out by the windings being arranged in a sinusoidal distribution, since they form a magnetic field with the same number of poles as the fundamental, and the winding distribution function is only able to substantially affect magnetic fields of greater number of poles than the fundamental.
In a high phase order concentrated winding machine, all temporal harmonics with a harmonic number lower than the number of phases are properly sampled, and produce on the stator a multi-pole rotating magnetic fields rotating with the same frequency and in the same direction as the fundamental. These temporal harmonics, on the stator, directly become spatial harmonics. However, since they rotate at the same speed and direction as the fundamental, they are desirable spatial harmonics, representing greater efficiency by causing extra beneficial torque in the rotor.
Temporal harmonics with a higher harmonic number than the number of phases will not be properly represented on the stator, and will produce magnetic fields with a number of poles different from double their phase number. For example, in a 17 phase 2-pole machine, the 19th harmonic would produce a 30-pole rotating field (15th harmonic of 2 pole) and in a 7 phase, 4 pole machine, the 9th harmonic would produce a 20 pole rotating field (5th harmonic of 4 pole). In a 7 phase 2-pole machine, the 13th harmonic would be a 2-pole rotating field. In the cases when the harmonic order exceeds the number of phases, the rotating field produced by this harmonic will not be properly represented. Instead a rotating field that is a non-corresponding harmonic of the fundamental rotating field will be produced. This field may rotate at a different direction from the fundamental and possibly in the reverse direction This is similar to temporal harmonics with a harmonic number greater than three in a three phase machine, in the fact that they represent detrimental torque. However, all the magnetic fields produced by these harmonics in the instances when the pole count is greater than the pole count of the fundamental, would be spatial harmonics of the fundamental, such as the 19th harmonic in the 17 phase, 2 pole machine, which produces a 30 pole rotating field, and the 9th harmonic in the 7 phase, 4 pole machine, which produces a 20 pole rotating field.
Temporal harmonics that are even or are multiples of the number of phases of the machine do not produce magnetic fields on the stator at all, due to symmetry and similar considerations.
Sampling and Reconstruction Filters
A bandwidth-limited continuous signal may be completely represented by a discrete series of samples, providing that this series of samples occurs frequently enough. The continuous signal may have an amplitude which changes over time, in which case the samples form a time series of measured amplitude versus integral time (e.g. 1 sample each second). The continuous signal may be an amplitude which changes with position, in which case the samples for a series of measured amplitude versus integral position, (e.g. 1 sample each meter). The period is arbitrary, and depends upon the signal being sampled. For baseband signals, the sampling frequency must be twice the maximum frequency present in the signal being sampled, otherwise aliasing may occur. Aliasing is when the signal being sampled contains frequency components that are outside of the allowed frequency range, in which case the results of sampling and reconstruction will be incorrectly produced, but allowed components.
Critical in the use of the sampling theorem is the use of the reconstruction filter. The reconstruction filter is a low pass filter that recreates the intermediate values of the original continuous signal using the data from the sample points. The winding of a motor is distributed according to a reconstruction filter. The rotating current structures, and thus the rotating magnetic filed structures are explicitly constrained by the form of the winding.